Session: Research Posters

Paper Number: 173207

Tipping the Balance: A Dynamic Systems Approach for Post-Hazard Community Recovery 

Human settlements, whether small towns or major urban centers, are continuously subject to perturbations. From wildfires and earthquakes to floods and hurricanes, natural hazards can disrupt physical infrastructure (roads, buildings, and utilities) and destroy the social fabric of communities. In the aftermath of natural hazards, households are forced to decide whether to repair and stay, or to permanently relocate, leaving behind empty dwellings. These microscale decisions can accumulate and shape macro level patterns of housing occupancy and vacancy, potentially triggering feedback loops that influence long-term neighborhood stability and the housing market, ultimately risking systemic decline [1]. At the core of this process is a network of coupled decision-makers, households, whose states evolve under the dual influences of individual risk perceptions and the attitudes of their neighbors [2,3], analogous to contagion processes in epidemiology [4]. Uncertainty in reconstructing these dynamics remains considerable, and unveiling the mechanisms that precipitate neighborhood scale transitions from recovery to abandonment poses an even greater challenge.

                Inspired by a larger class of contagion problems that include epidemiological models of disease spreading [5], we propose a dynamic systems framework to understand the mechanisms and thresholds that govern the community recovery at the macroscale. Specifically, we develop a mean-field compartmental model grounded in residential mobility studies [6], in which each house can be in one of four states: rooted (an intact home occupied by a household committed to stay), wishful (an intact home occupied by a household inclined to leave), damaged (pending repair), or vacant (an abandoned and/or available for re‑occupancy). Transitions between compartments follow probabilistic rules that include baseline rates and behavioral contagion, whereby the likelihood of being repaired or abandoned is influenced by the fraction of the corresponding household’s connections to others. This formulation allows the model to capture both positive (repair) and negative (abandonment) feedbacks, similar to models of innovation diffusion, where adoption utility increases with the number of adopters [7]. Through linear stability and bifurcation analysis, we identify that the strengths of the social influence and of migration intent are critical parameters that set a threshold at which the system undergoes a transcritical bifurcation. At this point, two equilibrium points exchange stability, marking a critical transition beyond which the system cascades into systemic vacancy.

This work is a first step towards a generalizable, scalable approach for modeling post-disaster housing dynamics that integrates engineering, urban science, network and behavioral theory. Importantly, we show that better connected communities are more resilient to long-term vacancy and have higher critical thresholds, highlighting the double role of network connectivity on system recovery and stabilization. By interpreting post-disaster recovery as a bifurcation problem, we pinpoint key parameter relationships that shed light into why some communities rebound while others decline.

 

[1] Negri, R., Dragomir, C., Xu, S., Porfiri, M., & Ceferino, L. (2025). Permanent relocation into and out of areas exposed to natural hazards: a Multidisciplinary review of the literature.

[2] Greer, A., Trainor, J., & McNeil, S. (2019). Voluntary household relocation decision making in the wake of disaster: Re-interpreting the empirical record. International Journal of Mass Emergencies & Disasters, 37(2), 197-226.

[3] Paul, N., Galasso, C., & Baker, J. (2024). Household displacement and return in disasters: A review. Natural Hazards Review, 25(1), 03123006.

[4] Keeling, M. J. (1999). The effects of local spatial structure on epidemiological invasions. Proceedings of the Royal Society of London. Series B: Biological Sciences, 266(1421), 859-867.

[5] Kiss, I. Z., Miller, J. C., & Simon, P. L. (2017). Mathematics of epidemics on networks. Cham: Springer, 598(2017), 31.

[6] Coulter, R. (2013). Wishful thinking and the abandonment of moving desires over the life course. Environment and Planning A, 45(8), 1944-1962.

[7] Arthur, W. B. (1989). Competing technologies, increasing returns, and lock-in by historical events. The economic journal, 99(394), 116-131.

Presenting Author: Ines Figueira New York University Tandon School of Engineering

Presenting Author Biography: Inês Figueira is currently a Ph.D. candidate in Mechanical & Aerospace Engineering with a track in Urban Science at NYU Tandon School of Engineering, where she is a member of the Dynamical Systems Laboratory and the Center for Urban Science + Progress (CUSP). She obtained her Bachelor’s degree in Aerospace Engineering at Instituto Superior Técnico of the University of Lisbon (Lisbon School of Engineering) in 2023.

Her research focuses on mathematical modeling applied to sustainability challenges in cities, with an emphasis on climate adaptation and urban crime dynamics. Inês studies complex urban systems and human behavior, developing data-driven models to improve understanding and support more effective responses to urban challenges.

Authors:

Ines Figueira New York University Tandon School of Engineering
Luis Ceferino University of California, Berkeley
Maurizio Porfiri New York University Tandon School of Engineering